18,853 research outputs found
C*-Structure and K-Theory of Boutet de Monvel's Algebra
We consider the norm closure of the algebra of all operators of order and
class zero in Boutet de Monvel's calculus on a manifold with boundary .
We first describe the image and the kernel of the continuous extension of the
boundary principal symbol to . If the is connected and is not empty,
we then show that the K-groups of are topologically determined. In case the
manifold, its boundary and the tangent space of the interior have torsion-free
K-theory, we prove that is isomorphic to the direct sum of
and , for i=0,1, with denoting the compact
ideal and the tangent bundle of the interior of . Using Boutet de
Monvel's index theorem, we also prove this result for i=1 without assuming the
torsion-free hypothesis. We also give a composition sequence for .Comment: Final version, to appear in J. Reine Angew. Math. Improved
K-theoretic result
Vortex-Antivortex Lattice in Ultra-Cold Fermi Gases
We discuss ultra-cold Fermi gases in two dimensions, which could be realized
in a strongly confining one-dimensional optical lattice. We obtain the
temperature versus effective interaction phase diagram for an s-wave superfluid
and show that, below a certain critical temperature T_c, spontaneous
vortex-antivortex pairs appear for all coupling strengths. In addition, we show
that the evolution from weak to strong coupling is smooth, and that the system
forms a square vortex-antivortex lattice at a lower critical temperature T_M.Comment: Submitted to Physical Review Letter
Conditions for free magnetic monopoles in nanoscale square arrays of dipolar spin ice
We study a modified frustrated dipolar array recently proposed by M\"{o}ller
and Moessner [Phys. Rev. Lett. \textbf{96}, 237202 (2006)], which is based on
an array manufactured lithographically by Wang \emph{et al.} [Nature (London)
\textbf{439}, 303 (2006)] and consists of introducing a height offset
between islands (dipoles) pointing along the two different lattice directions.
The ground-states and excitations are studied as a function of . We have
found, in qualitative agreement with the results of M\"{o}ller and Moessner,
that the ground-state changes for , where ( is the
lattice parameter or distance between islands). In addition, the excitations
above the ground-state behave like magnetic poles but confined by a string,
whose tension decreases as increases, in such a way that for
its value is around 20 times smaller than that for . The system exhibits
an anisotropy in the sense that the string tension and magnetic charge depends
significantly on the directions in which the monopoles are separated. In turn,
the intensity of the magnetic charge abruptly changes when the monopoles are
separated along the direction of the longest axis of the islands. Such a gap is
attributed to the transition from the anti to the ferromagnetic ground-state
when .Comment: 6 pages, 7 figures. Published versio
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